16k views

### Logarithmic scale in a DensityPlot and its legend

I was recently faced with the task of creating a DensityPlot with a logarithmic colour scale, and with providing it with an appropriate legend. Since I could not find any resources to this effect on ...
6k views

### Complex valued 2+1D PDE Schrödinger equation, numerical method for NDSolve?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schrödinger) equation, for the free particle propagation of an initial wavepacket. ...
4k views

### Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
2k views

### Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
4k views

### Circular membrane vibration simulation

I'm new in Mathematica and I'm trying to simulate the vibration of a circular membrane for math project but I don't even know how to start. The wave equation describes the displacement of the ...
1k views

### Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
553 views

### Numerically solving Helmholtz equation in 2D for a Guitar

Hi I am new to using Mathematica, so am not too confident. I am essentially trying to model vibrations of a guitar sound board for a project. It would be great to get some visualisations of the ...
653 views

### Gaining precision/accuracy with NDEigenvalues

See further down for an important note Background I study (one component of) the semi-classical Pauli operator, $$P_h=-h^2\Delta+ih(-y,x)\cdot\nabla+\frac{x^2+y^2}{4}-h.$$ For this particular ...
414 views

### Schrödinger equation for a hydrogen atom and lack of memory

I'm trying to solve the Schrödinger equation for a hydrogen atom in the Cartesian coordinate system. This is my code ...
1k views

### Comparing analytical solution with numerical solution of Helmholtz equation in a unit square

I am just learning PDE, and I am interested to compare analytical solution with numerical solution of Helmholtz equation in a unit square with zero boundary condition. I am not sure if it possible. ...
238 views

### NDEigenvalues complains not Hermitian with large dimension differential operator

The following snippet calculates eigenvalues and eigenfunctions of a null operator (just as an example): ...
290 views

### Inconsistent behaviour between Active and Inactive forms of PDEs (finite element method)

Bug introduced in 13.0 or earlier and fixed in 13.1.0 I have been using the finite element tools in Mathematica version 13.0 to solve eigenvalue problems in physics (Schrödinger equation) using ...
605 views

### Finding eigenvalues for Laplacian operator for 3D shape with Neumann boundary conditions

I've just begun to use the Mathematica so my question may seem to be naive. To get a solution for my problem I looked at the example provided in help. ...
97 views

### NDEigensystem: 1D problem with discontinuous coefficients

I am trying to use NDEigensystem to solve the 1D problem -cs[x]^2 vx''[x] = w^2 vx[x] with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...